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Smoothing One-Dimensional Foliations on S1 x S1

Published online by Cambridge University Press:  20 November 2018

Maurice Cohen
Maurice Cohen*
Affiliation:
Sir George Williams University, Montreal Quebec
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Letf:S1→S1 be an orientation preserving C1-diffeomorphism. Denote by the flow on S1 x S1 which is the suspension of f(see Smale [5]).

We consider the problem of approximating by a smoother foliation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 43 - 44
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Cohen, M., Approximations of foliations, Canad. Math. Bull. (3) 14 (1971), 311–314.Google Scholar
2. Denjoy, A., Sur les courbes définies par les equations différentielles à la surface du tore, J. Math. Pures Appl. (9) 11 (1932), 333–375.Google Scholar
3. Reeb, G., Sur certaines propriétés topologiques des variétés feuilletées, Act. Sci. et Ind., 1183, Hermann, Paris, 1952.Google Scholar
4. Schwartz, A. J., A generalization of a Poincaré-Bendixon theorem to closed two-dimensional manifolds, Amer. J. Math. 85 (1963), 453–458.Google Scholar
5. Smale, S., Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.Google Scholar
6. Van Kampen, E. R., The topological transformations of a simple closed curve into itself, Amer. J. Math. 57 (1936), 142–152.Google Scholar